The present invention relates to an apparatus for calculating the electromagnetic field intensity that calculates the electromagnetic field intensity by dividing a target device into a plurality of patches based on a moment method and using a mutual impedance or a mutual admittance between the patches, and a method for calculating the electromagnetic field intensity. Further, this invention also relates to a computer-readable recording medium in which programs for allowing a computer to execute the method for calculating the electromagnetic field intensity are recorded. More particularly, this invention relates to a technology of calculating the electromagnetic field intensity with which the mutual impedance and the mutual admittance between the patches can be calculated efficiently and at high speed.
In simulating the intensity of an electromagnetic wave radiated from an object in the conventional art, there has been frequently used a moment method, i.e., one of integration methods derived from the Maxwell""s electromagnetic wave equation, in which an electric current or a magnetic current is calculated by dividing the object into small elements.
FIG. 1 shows how the electromagnetic field intensity is calculated in the moment method. As shown in this figure, a target device is modeled as the set of minute dipoles, and then, the electromagnetic field intensity is obtained by calculating a mutual impedance between a pair of dipoles.
Specifically, mutual impedance Zdipole between a pair of dipoles is computed based on the following equation:
Zdipole=Z00+Z01+Z10+Z11
Therefore, in order to obtain the mutual impedance between the dipoles, it is necessary to obtain a mutual impedance between monopoles.
FIG. 2 shows how the mutual impedance is calculated conventionally. As shown in this figure, a patch is considered as the set of linear conductors (monopoles), and mutual impedance Zij between the monopoles is computed.
The mutual impedance zij includes four kinds of mutual impedances Zij00, Zij01, Zij10 and Zij11 corresponding to the positions of patches adjacent to a patch 1 and a patch 2, so that the mutual impedance Zij between the monopoles is expressed by a double integration along each of the monopoles as follows:
Zij=∫∫{(xcexc/4xcfx80)IiIj+(1/4xcfx80xcex5)qiqj}exe2x88x92jkt/rdxdXxe2x80x83xe2x80x83(1)
wherein Ii, Ij represent electric currents flowing in monopoles i and j and qi and qj represent charge distribution; ∫∫ represents double integration in which the result obtained by integration from x0 to x1 is further integrated from X0 to X1; Ii and qi are functions of x; and Ij and qj are functions of X.
The above-described double integration is calculated using the exponential integration method or the fast reaction matching moment method (hereinafter referred to as FRM method) disclosed in Japanese Patent Application Laid-open No.11-15184. Subsequently, integration is performed using the Gauss integration method for every patch along the direction in which the monopoles forming the patch are aligned. The Gauss integration method is one kind of numerical integration method in which the portion where integration is performed is divided into elements, and the resultant divided elements each are multiplied by an appropriate weight, to be added together.
In calculating the mutual impedance between the patches, the number of divided patch elements corresponds to the number of monopoles constituting the patch, and depends upon the shape of the patch and the distance between the patches. The greater the number of divided patch elements, the more accurate will be the calculation. However, since the number of additions of the mutual impedances between the monopoles is increased, a time required for the calculation becomes longer.
For example, in the case shown in FIG. 2, the mutual impedance between the patch 1 and the patch 2 is computed using the following equation:
xe2x80x83Zij=∫∫ ∫∫{(xcexc/4 z )IiIj+(1/4xcfx80xcex5)qiqj}dxdXdydYxe2x80x83xe2x80x83(2)
wherein ∫∫ ∫∫ represents quadruple integration in which the result obtained by integration from x0 to x1 is integrated from X0 to X1, and then, the result obtained by further integrating the above-integrated result from y0 to y1 is further integrated from Y0 to Y1.
In this way, the mutual impedance between the patches is calculated by obtaining the sum of the mutual impedances between the monopoles constituting the patch, thereby making it possible to calculate the electromagnetic field intensity.
However, when the electromagnetic field of the electromagnetic wave radiated from the model is obtained with high accuracy in the above-described conventional art, there is a problem that the number of patches constituting the model becomes great, so that the numerical integration (the Gauss integration) requiring a considerable time must be repeated, resulting in the necessity of an interminable processing time.
Particularly, on the assumption of a large-scaled model close to the actual situation, the number of patches constituting the model is markedly increased, requiring an interminable time for the Gauss integration. This is not practical.
Thus, when the electromagnetic field intensity is to be computed by using the moment method, it is remarkably important to efficiently compute the mutual impedance between the patches at a high speed.
When dielectric patches are used instead of metal patches, it is required to calculate the mutual admittance of the electric current flow and the magnetic current of the dielectric surface, consequently increasing the time taken to calculate the electromagnetic field. Therefore, it is remarkably important to efficiently compute the mutual admittance at high speed.
It is an object of this invention to provide an electromagnetic field intensity calculating apparatus which can efficiently compute a mutual admittance and a mutual impedance between patches at a high speed in the case where an electromagnetic field intensity is computed by using a moment method, an electromagnetic field intensity calculating method, and a computer-readable recording medium in which programs for allowing a computer to execute the electromagnetic field intensity calculation method are recorded.
According to one aspect of this invention, the mutual impedance between the patches can be efficiently computed at a high speed since it is computed based on the previously computed analytic solutions of the quadruple integration under the condition that the patches are rectangular in shape and are parallel or perpendicular to each other and the electromagnetic field intensity is calculated based on the computed mutual impedance.
According to another aspect of this invention, the mutual admittance between the patches can be efficiently computed at a high speed since it is computed based on the previously computed analytic solutions of the quadruple integration under the condition that the patches are rectangular in shape and are parallel or perpendicular to each other and the electromagnetic field intensity is calculated based on the computed mutual admittance.
A still another aspect of the invention provides a computer-readable recording medium in which are recorded programs for allowing a computer to execute an electromagnetic field intensity calculating method for calculating electromagnetic field intensity. According to this invention, a computer can execute the operations of computing the mutual impedance between the patches based on the previously computed analytic solutions of the quadruple integration under the condition that the patches are rectangular in shape and are parallel or perpendicular to each other and calculating the electromagnetic field intensity based on the computed mutual impedance.
Other objects and features of this invention will become apparent from the following description with reference to the accompanying drawings.